STAT 462
Geometric Distribution
(1-p)^(y-1)*p
Uniform Distribution (continuous)
1/(theta2-theta1)
Standard Normal distribution
1/Sqrt(2pi)*e^-(z^2/2)
Expected Value & Var -Uniform
E[x]=(theta2+theta1)/2. Var[x]= (theta2-theta1)^2/12
Expected Value & Var -Geometric
E[x]=1/p Var[x]=(1-p)/p^2
Expected Value & var -Beta
E[x]=alpha/(alpha+beta)
Expected Value & Var -Poisson
E[x]=lambda. Var[x]=lambda
Expected Value & Var -Binomial
E[x]=np Var[x]=np(1-p)
Expected value -Hyper Geometric
E[x]=nr/N
Expected Value & Var -Negative Binomial
E[x]=r/p. Var[x]=r(1-p)/p^2
Lambda(alpha)
Integral infinity to zero (y^(alpha-1)e^-y) dy
Negative Binomial Distribution
y-1Cr-1*P^(r-1)*(1-p)^(y-r) Y= attempts. R=Successes
Beta Distribution
y^(alpha-1)(1-y)^(beta-1)/beta(alpha,beta)
Z score
z= x-mean/standard dev
Normal Distribution
[1/omega*Sqrt(2pi)]*e^[-(y-mu)^2/2*omega^2]
Hyper Geometric Distribution
[rCy*N-rCn-y]/NCn N=total items n=sample r= items with characteristic
Gamma, Exponential, and Chi-Square Distributions
[y^(alpha-1)*e^-(y/beta)]/[beta^alpha *lambda(alpha)]
Chi-square distribution
alpha =v/2 beta =2
Exponential Distribution
alpha=1
Poisson Distribution
lambda^y/y! *e^-y
Binomial Distribution
nCy*p(y)^y*(1-p)^(n-y)